2.      You seem to imply that the GBFS provides a more reliable picture of sparrowhawk colonisation than the Newton & Haas data. I am afraid  I disagree about that, especially considering the very modest numbers of urban gardens involved particularly in zones 1 & 4. You suggest that incidence functions are similar for zones 2 and 3 (Fig 2b) but doesn’t table 1 indicate that these are the only pair of zones to show significantly different trends? (Table 1). Wouldn’t you therefore expect differences in sparrow trends between regions 2 and 3? Yet the sparrow trends are almost identical for these two zones.

3.      The contrast in conclusions between your study and several others (to which we can now add Newson et al, 2010) remains stark. You contest that your improved definition of hawk establishment provides the explanation for these contrasting conclusions, although Newson et al went to great lengths to provide a robust measure of hawk settlement and could detect no impacts on house sparrows. Your point about the Thompson method being potentially misleading seems only to apply to the non-censored data and a poorly fitting model. Both methods give similar results when the few gardens causing poor model fit were excluded. 

Another possible explanation for the different conclusions drawn by you and Newson is the different type data you have used. Your reliance on winter garden counts throws up interpretational caveats that do not apply to the same extent to breeding season data. As you know, sparrows are highly faithful to breeding sites between years but are much more mobile outside of the breeding season and might well avoid localities having high hawk activity. Or, alternatively, may become much less detectable in areas of high hawk activity. You suggest the form of the PC relationship argues against such a behavioural response but the actual form of any such response is unknown. A reduced frequency of usage of gardens with high hawk activity, by a flock/colony of constant size would cause average winter-long counts to fall. More generally, your use of the mean count across 26 weeks raises further problems of interpretation. For example, a decline in the mean count across years might simply reflect a shift in the timing of mortality of sparrows to earlier in the autumn/winter (possibly linked to hawk predation), and may not reflect any overall increase in over-winter mortality or any subsequent reduction in recruitment or local population size.

You seem to overstate the strength of your predictive models when you claim that ‘sparrowhawk incidence explains practically all of the variance in sparrow numbers’. You don’t seem to present the variance statistics for the zonal analyses (and see my comments above about the inconsistencies in trends relating to the urban data), while the hawk variable only accounts for a modest reduction in deviance compared to a temporal trend (after site effects, time accounts for 28% of the remaining deviance while hawk PC accounts for 35%, leaving 65% of the deviance unexplained; Table 3). So compared to the temporal model, the hawk effect only accounts for an additional 7% of the deviance. You don’t seem to have subjected the PC analysis to model criticism and your usage of the AIC to support the PC model ignores well known fundamental objections to the use information theoretic approaches for the comparison of fixed effects within a mixed modelling framework (e.g. Gurka 2006). Your PC analysis is based on only 54 sites which (given the ratio of urban-rural sites in Fig. 1) suggests a very small number of contributing urban sites (perhaps a similar number to that for urban zone 4 which you acknowledge ‘may not provide an accurate summary of the underlying trends’). I am also curious as to why sparrow counts showed large and significant declines several years before the first arrival of the hawk (AP transition in Fig. 3).   

To conclude, I believe your paper constitutes a useful and interesting contribution to the ongoing debate on causes of house sparrow decline. However, I believe you are overstating the strength of the evidence that your analyses / data provide, and you seem to be reluctant to acknowledge evidence (or consider alternative hypotheses) that run contrary to your favoured hypothesis. For this reason, I am not surprised that all three judges advised against the Independent awarding its prize for your paper.

Newson S.E., Rexstad Eric A., Baillie, S.R., Buckland S.T. & Aebischer N.J. 2010. Population change of avian predators and grey squirrels in England: is there evidence for an impact on avian prey populations? Journal of Applied Ecology 47, 244-252. 10.1111/j.1365-2664.2010.01771.x

Gurka, M.J. (2006. Selecting the best linear mixed model under REML. Am. Stat. 60, 19-26.

(1) The reason you don’t agree that the absence of the patterns you predict is ‘supremely irrelevant’ is that they arise from your hypothesis and not ours. The fact that the data refute your hypothesis cannot be put forward as a criticism of our paper. We did not bother to test your hypothesis for the very good reason that it is clearly wrong, and based on the following erroneous premises: (i) That the re-occupation of Newton’s four zones by Sparrowhawks happens sequentially and instantaneously, like the switching on of a light; and (ii) that Sparrow populations are at a stable equilibrium before the Sparrowhawks’ arrival. Only these circumstances will fulfil your ‘clear hypothesis of the pattern of decline’ that sparrow trends should be more negative in areas recolonised by Sparrowhawks and occur later in areas recolonised later. However Sparrowhawk recolonisation is not instantaneous, but is occurring at rates that vary both between and within zones throughout the study period, which is why a simulation model is necessary to compare population trends in the two species.

(2) You are suggesting it would have been better to try an approach which enabled confidence limits to be applied to P, and better still to develop a model with a range of additional variables to ‘take account of’ other potential explanatory factors. You have outlined your alternative approach in only the vaguest terms (and I would urge you to clarify it), but I suspect that even if predation mortality were the only explanatory variable, it would not emerge as significant, adding yet another example to the litany of studies that have shown ‘no relationship’ between predator and prey numbers.

The common characteristic of all such studies is that no relationship emerges because they fail to partition signal from noise. This is why we have taken a different approach that recognises the triviality of trying to assess the significance of P, which can only be zero if Sparrowhawks never kill any Sparrows. We ask, given a value of P<1 and empirically determined values of r and N₀, what are the values of K that provide the best fit to each of the eight sparrow trends? We then determine the P that provides the best overall fit, and ask whether this is likely to have occurred by chance.

We do not assign a probability because there is no objective means of assigning a reasonable a priori range of variability in sparrow trajectories. However, it is clear that the number of sets of eight Sparrow trajectories that would produce a worse fit than that observed is essentially infinite, but that a very limited range of sets that would produce a better fit, so that there is a minute probability that such a fit could emerge by chance. The modelling approach also captures the biological reality that regional trends are a composite of widely varying trends in individual sites, which I suspect your suggested approach would not.

(3) You have fallen into a semantic trap here. Remember this is GBFS data – sites classified as ‘rural’ are merely those in which less than half the surrounding 4km² is ‘built up.’ All of these data are associated with dwellings, and even those classified as rural show differences on average from CBC data derived from genuinely rural sites. GBFS data both here, and in previous BTO publications show stable Sparrow populations up to the mid-1980s, while CBC data show declines starting in the 1970s (e.g. Siriwardena et al. 2002). By this token all of the data we use are urban. I should also note that the challenge set by the Independent was to ‘explain the House Sparrow’s recent precipitous decline, especially in towns and cities.’

(4) One needs to recognise that other variables may be neither important nor quantifiable, and that if they can’t be quantified, as may ultimately be the case with food availability and nest sites, they do not fall within the realm of science. Your position that nothing can be inferred until every conceivable variable has been exhaustively investigated is appropriate if the objective is to generate a ‘need’ for ever more research, but not if it is to find solutions to problems. However you are also inconsistent in the application of your principles. The BTO has never been slow to infer the importance of food availability in Sparrow decline, despite the lack of controls in studies purporting to demonstrate this. In fact there is no evidence that food or nest sites are a factor, and what can be asserted without evidence can also be dismissed without evidence.

(5) You have reverted to your original position, which is that GBFS data do indeed provide a good population index for House Sparrow, but you now complain that we do not have sufficient urban sites. Leaving aside both the semantic issue and your misinterpretation of the competition criteria, both discussed at (3), the shortage of ‘urban’ sites only applies to the analysis in relation to PC transition. For the other analyses there is very adequate ‘urban’ representation, as can be determined from Figure 1. If, as you say, this is your major concern, there is no basis for it.

We have shown that both the general decline in Sparrow populations, and all of the major variations in the trajectory of this decline, can be satisfactorily explained by Sparrowhawk predation without the need for any additional variables. The fact that ‘other changes’ are happening in the environment does not invalidate this, since despite the huge investment by the BTO and others there is no critical evidence that any of these changes has any relevance. By all established standards of scientific inference, Sparrowhawk predation is the explanation for House Sparrow decline.

(1) You assert that our paper is not convincing because other papers have inferred that food shortage is responsible for House Sparrow decline. I should probably note in passing that if you intend to deploy this argument consistently, you will automatically disqualify any entry to the Independent’s competition that fails to support the explanation preferred by the RSPB. You state that a lack of discussion of the food shortage hypothesis is a weakness of the paper. You will also be aware of the demands of journal editors, and we were specifically instructed to remove such discussion to shorten the paper and focus on the results of the analysis. I will therefore take the opportunity here to discuss the studies you have cited.

The Hole et al. (2002) paper is difficult to evaluate, since it provides no details whatever on the methodology of the supplementary feeding experiment. The results as presented are of little value, since although they are consistent with the proposition that food shortage caused low survival at University Farm in the winter 1998-9, they are also consistent with the proposition that supplementary feeding in 1999-2000 increased survival by reducing the sparrows’ need to expose themselves to Sparrowhawk predation. The farm is adjacent to Wytham Woods, to which Sparrowhawks returned as a breeder in the interim between the study of Dawson (The breeding biology of the House Sparrow. D.Phil. Thesis, University of Oxford, 1972) and that of Hole, during which the Sparrow population at the farm underwent a marked decline.

The Peach et al. (2008) paper demonstrates a relationship between aphid density and breeding success among House Sparrows breeding in nest boxes over three years in Leicester. The only inference that can be drawn from this is that breeding success is limited by food availability, which is a trivial result since this is always the case, no matter if a population is declining, stable, or increasing.  The study therefore tells us nothing about the cause of House Sparrow declines.

The trend towards smaller brood sizes derived from nest record cards is presumably that reported in Crick & Siriwardena (2002). Mean brood size estimates are plotted on p 169 of that paper for the years 1976-2000, and range between 2.7 and 3.7. The lowest estimate occurs in the year 2000 at the very end of the data sequence, following a run of three years in which estimates range from 3.2-3.5. The allegedly significant downward trend is therefore purely a function of leverage – I have checked this myself by reading the data from the figure and performing a regression, which is very far from being significant if the year 2000 estimate is deleted. The more pertinent trend is that of increased productivity per nesting attempt as shown on page 171 of Crick & Siriwardena, which is consistent with a trend of increasing food availability related to improved summer weather conditions, especially warmer and drier summers, as indicated by the very similar trend emerging from the model of productivity versus weather conditions in Peach et al. (2008).

Your hypothesis that the relationship between Sparrowhawk establishment and the beginning of Sparrow decline is a function of an influx to gardens of species which (i) outcompete House Sparrows and (ii) attract Sparrowhawks, is ingenious and I would be intrigued to see you develop the idea. Which species do you think might be outcompeting House Sparrows for nest sites? Which species have flooded into gardens/outcompeted sparrows for food/proved irresistible to Sparrowhawks? Why has the influx of these species followed the same spatio-temporal pattern as Sparrowhawk recolonisation? I might also add that in order to factor in abundance of other species I should have needed access to the data, but since it took over a year to persuade the BTO to release the data for the two focal species I may well have still been waiting to begin the study you propose.

(2) You complain that the spatio-temporal correspondence of Sparrowhawk and House Sparrow is “not quite as clear as claimed,” and single out urban zones 2-4. You state that the similarity of House Sparrow trends in zones 2-4 differs from that which would be predicted by Sparrowhawk incidence because Newton’s data on the latter predict a sequence of zone 2 followed by zone 3 followed by zone 4. However, Newton did not differentiate urban and rural habitats, and you can only maintain your position by ignoring Figure 2B, which shows a very similar Sparrowhawk incidence function in urban zones 2&3, which parallels the similar trajectories of the corresponding Sparrow populations. Contrary to your assertion, we do not claim that there is a close correspondence between the two species in urban zone 4, and I would refer you to paragraph 3 of the discussion: “In the one instance in which it proved impossible to derive a close approximation of sparrow population trajectory from sparrowhawk incidence, that for urban sites in zone 4, the estimated trends for both species were based on data from only eight sites and so may not provide an accurate summary of the underlying trends.”

(3) You state that you are confused by the contrast between the results we present and those of Thomson et al. (1998), and Chamberlain et al. (2009). However we provide a comprehensive explanation for these differences, and you may find it rewarding to re-read paragraphs 4 & 5 of the discussion in this regard. The Thomson analysis uses raw Sparrowhawk presence and absence data as an explanatory variable, and we show how this can be misleading by demonstrating an apparent lack of relationship when it is applied to the GBFS dataset (top line Table 4). Chamberlain assumed continuous Sparrowhawk presence after the first appearance of the species at a site (which we refer to as the AP transition), and again we show how this can be misleading by demonstrating an apparent lack of relationship using this approach (top line Table 2, Figure 3). When these analyses are repeated using the PC transition (first year of continuous presence), strong relationships emerge between the two species in both analyses (bottom half of Table 4, Table 3/Figure 3).

You state that “the observed reductions in House Sparrow counts simply reflect an avoidance of gardens used a lot by Sparrowhawks.” However, both in the case of the spatio-temporal analysis (Figure 2), and the presence-absence analysis (Figure 3), Sparrowhawk incidence explains practically all of the variance in Sparrow numbers. Chamberlain et al. (2005) demonstrated a very high degree of correlation between GBFS and CBC indices for the House Sparrow, so If the decline in the former is attributed to avoidance, this must also apply to CBC, and you must therefore believe that there has been no population decline in the species? Furthermore, it is apparent from Figure 3 that the decline in House Sparrow numbers following Sparrowhawk appearance takes place gradually over a period of 15-20 years, which is the signature of a population process rather than a behavioural response which would be instantaneous, and produce a step change pattern in Figure 3.  Finally you are mistaken in referring to both Thomson and Chamberlain as looking at breeding populations, since Chamberlain uses GBFS data.

This paper is a comprehensive analysis of the BTO’s long term (1970-2004) winter garden bird counts scheme – the Garden Bird Feeding Survey (GBFS). A recently published analysis using the same data, but a different method (Chamberlain et al. 2009), found no coincidence between the timing of house sparrow (HS) declines in gardens, and the timing of recolonization by sparrowhawks (SH). This new study has analysed the same data in a more sophisticated way. It has found that the timing of HS declines in gardens does coincide quite closely with the local establishment (rather than first arrival) of SHs.

This lends support to the assertion that HS population declines have been caused by the return of the SH to central and eastern Britain during the 1970s and 1980s. This paper is of general interest, as it is one of the first studies to provide evidence of possible impacts of SHs on songbirds.

The authors of the paper are to be congratulated on the rigorousness of their analyses.

The £5,000 prize offered by the Independent is for “a paper published in a peer-reviewed scientific journal which explains the disappearance of the house sparrow from Britain’s towns and cities.” On the basis of this paper, and other papers, I am not convinced that predation by sparrowhawks alone explains the house sparrow's disappearance. I have three main areas of reservation:

First, previously published studies have provided evidence that other factors are limiting HS numbers in Britain, and might well have contributed to the population decline. In particular, lack of seed and grain on farmland (Hole et al. 2002) has been shown experimentally to limit overwinter survival and to reduce local sparrow populations. Similarly, a lack of invertebrates in urban-suburban areas causes low reproductive success (Peach et al. 2008). Evidence from BTO nest record cards of declining average brood sizes in house sparrows is consistent with the hypothesis of declining invertebrate availability in towns and cities. It is a little strange that Bell at al. do not acknowledge either the Peach et al. study or the BTO nest record cards evidence.  More broadly, a general weakness of the Bell study is that it only addresses one candidate hypothesis to explain the HS decline. Had they considered other candidate causes, they might have found stronger relationships, or perhaps relationships that were confounded with the arrival of hawks (e.g. changes in the abundance of species that might compete with HS for nest sites or food, and perhaps attract hawks to gardens).

Second, the associations between HS and SH outlined by Bell et al. are not quite as clear as claimed. In particular, the timing and magnitude of the HS declines looks remarkably consistent across some regions, even though the timing of recovery of SH populations differed markedly. For example, the pattern of declines of urban HS in regions 2-4 are all very similar (Figure 2D). However, Newton's data on SH recovery would predict that HS declines should have happened in region 2 first, then 3, followed by 4 if SH predation was limiting HS numbers.

Third, and most importantly, I am aware of three other similar correlational studies, two published (Thomson et al 1998; Chamberlain et al 2009), and one in press, that come up with a different conclusion, i.e. no impact of sparrowhawks on house sparrow numbers. While Bell and his colleagues may argue that their analysis is more sophisticated, the presence of conflicting answers leaves the conservation practitioner confused. An inherent weakness of the Bell et al paper is that it only looks at wintering, rather than breeding populations of sparrows. It is possible, therefore, that the observed reductions in HS counts simply reflect an avoidance by HS of gardens used a lot by SHs. Both other studies that have looked at SH impacts on HS breeding populations have found no effect.

It is entirely possible that sparrowhawk predation has contributed to the decline of the house sparrow in Britain. However, given the conflicting evidence from correlational studies, I cannot conclude that sparrowhawk predation alone has caused the decline of the house sparrow. This paper does, however, increase the likelihood that SHs may be implicated in the decline of HSs, and provides justification for carefully planned field studies to look for such impacts. 

(1) You devote more than a quarter of your review at point 1 to a refutation of the proposition that significant differences in sparrow population trends among the eight contingencies of region/rurality provide evidence of an effect of sparrowhawk predation. I’m afraid this is a straw man. We state quite explicitly that the pattern provides no such evidence, and the analysis referred to is merely a preliminary to the modelling exercise, which you refer to at point 2. For this exercise to be meaningful, it is first necessary to establish that there are statistically significant differences among the eight contingencies, otherwise we cannot be sure that there are any differences to explain.

You erroneously state that we are testing whether sparrow population trends “are more negative in areas which sparrowhawks have re-colonised and does this downward trend occur later”. As a population biologist, I am sure you are aware that there is no reason to assume such a simple pattern of variation between predator and prey among different regions and habitats, since the underlying dynamics of prey populations may vary, as does the temporal pattern of Sparrowhawk incidence among the eight contingencies. The fact that later declines in rural areas are not “startlingly obvious”, or that urban patterns are similar, is therefore supremely irrelevant.

(2) You state that you find the results of the simulation model unconvincing because there is no test of the probability of the observed model fit. You must be aware that this presents an intractable statistical problem, not least because we are attempting to predict the fitted values of one model using fitted values from another model. The fact that we have failed to do something that may well be impossible is not a valid criticism.

You state that the observed fit could be obtained for “simple mathematical reasons,” but you also state that it would have been better to employ a model with “greater biological realism.” You will be aware that increasing the number of parameters in the model makes it easier to fit to any observed data set, and that if the number of parameters is large enough a model can be fitted to any conceivable dataset ‘for mathematical reasons’. Your position appears to be that our model therefore has too many parameters to be plausible on mathematical grounds, but too few to be realistic on biological grounds. If you apply this consistently, you must surely regard the whole of population biology to be invalid?

The justification for the inference we draw from this model can be stated in quite straightforward terms.

·                     Rural Sparrows/Sparrowhawks in 1970-74 are ordered zone 4>3>2>1/zone 1>2>3>4.

·                     Sparrows/Sparrowhawks in rural zones 1 and 2 decline/increase in a linear and converging fashion.

·                     Sparrows/Sparrowhawks in rural zone 3 undergo a decline/increase that accelerates, then stablilizes.

·                     Sparrows/Sparrowhawks in rural zone 4 are increasing/absent, then stabilize/appear, then undergo an accelerating decrease/increase with a suggestion of stabilization at the end.

·                     Sparrows/Sparrowhawks in urban zone 1 are increasing/absent, stabilize/appear, then undergo an accelerating decrease/increase with no sign of stablilization.

·                     Sparrow/Sparrowhawk populations in urban zones 2 & 3 are initially stable/nearly absent, then decelerate/accelerate to a roughly linear decline/increase.

Urban zone 4 proves to be the exception. Sparrows vary in a similar fashion to those in urban zones 2-3, but Sparrowhawks appear to be absent for most of the data period, appearing in only a small proportion of sites at the end.  This is an exception that proves the rule, however. Unlike in urban zones 2-3, Sparrow numbers in urban zone 4 are statistically stable until the 1990s, and the Sparrowhawk trajectory in urban zone 4 is not significantly different from that in urban zone 3. The lack of fit therefore does no damage to the model, but skewers the proposition that the good overall fit represents a mathematical artifact by demonstrating how very easy it is for best fit trajectories to vary in a fashion that cannot possibly be reproduced by the model.

The statistical models for the two species are completely independent, and the proposition that the correspondence of the varied trajectories shown by the two species in 7 out of eight contingencies is likely to have occurred by chance is simply and plainly untenable. On a purely instrumental level, any alternative causal factor would have to be at least an equally good predictor of sparrow population trends. If the BTO/RSPB explanation of a complex interaction of agricultural/urban development variables is preferred it would have to provide a very much better explanation of variance in sparrow numbers, which is clearly highly unlikely. If you are consistent therefore, you will never find any explanation acceptable.

(3) You erroneously state that there is no information on ‘geographical spread’ of the sites in the analysis shown in Figure 3 and Table 3. Though you do not say so clearly, you are attempting to imply that the superiority of PC-centred time over chronological time as an explanatory variable is an artifact of an underlying correlation of PC transitions with an unknown causal factor with an E-W gradient.  However in the same breath you acknowledge that this is unlikely to be the case, because the wished for information on geographic spread is indeed incorporated in the analysis, which shows that the relationship holds within each of the four geographic zones. Your complaint that there is no analysis of urban rural gradient is spurious, since only a handful of the 54 sites with a PC transition were urban, rendering such an analysis meaningless.

(4) You complain that the analysis in table 4, which implements a modified application of the approach in Thomson et al. 1998, does not differentiate urban and rural. As above, this carries no weight because of the small number of urban sites available in the PC transition sample. Even were this not the case we would not have factored in rurality, since our objective was to follow Thomson, who did not differentiate habitats, in order to demonstrate the drawbacks in his approach.

You state that the results do not reliably reflect an effect of Sparrowhawks on Sparrow population size, since Sparrows could be merely avoiding gardens where Sparrowhawks occur. There are two important problems with this argument. Firstly, figure 3 indicates that there is no evidence of Sparrow decline prior to the establishment of Sparrowhawks, and that the decline can be explained in its entirety by Sparrowhawk presence. If this is explicable in terms of avoidance, it follows that there has been no ‘real’ decline in Sparrow numbers, which we know not to be true.  Secondly, there is a steady decline in Sparrow numbers over a period of almost 20 years following Sparrowhawk establishment. Do you really maintain that Sparrows react to the appearance of a predator by gradually drifting away from a feeding station over a period of two decades? Do you not think instead that the signature of a behavioural response would be an abrupt step-down in numbers at the PC transition?

You state that no inferences can be drawn about the effects of Sparrowhawk predation without accounting for variation in nest site and food availability. The difficulty of quantifying these two variables means that you effectively insure yourself via this argument from ever having to concede the significance of Sparrowhawk predation. Even if such quantification were possible, you could logically fall back on the need to account for weather, disease, parasites, atmospheric pollution, competitors or any other conceivably relevant variable. Indeed, your position applied consistently would prevent you from ever drawing inferences from any ecological study.

Finally, here are some quotes from papers published previously by the BTO:

“Thomson et al. (1998) demonstrated that between-year changes in abundance of a wide range of bird species on CBC plots were not related to the presence or absence of Sparrowhawks on the census plots. Unfortunately, this study did not include House Sparrow, and it would be a useful exercise to repeat this type of analysis for House Sparrow and to perhaps to (sic) undertake a similar study using data from GBFS gardens.” (From Crick, Robinson & Siriwardena 2002, p279).

“GBFS is likely to be useful in monitoring species that are associated especially with human habitations and which show a marked population change (e.g. declining Starling and House Sparrow).” (From Chamberlain, Vickery, Glue, Robinson et al. (2005), which also reports a correlation of 0.967 between GBFS and CBC data for House Sparrow over the period 1970-2000).

We have performed the analysis suggested by you in the first quote, which comes from a paper discussing the potential causes of Sparrow decline. Why do you now consider the results to be unreliable? When did you resile from the opinion you express in the second quote, and what level of correlation between GBFS and CBC would be required to ‘make the link’ between numbers in gardens and population size?